Despite spending long spells of the match on the back foot, Evian came close to taking an early lead when Yeltsin Tejeda fired just wide of the target from a tight angle.
The visitors looked threatening throughout the first half, but the opening goal did not arrive until the 42nd minute, with Jordan Veretout stepping up to drill home a penalty after Cedric Mongongu had brought down Serge Gakpe.
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Nantes were forced onto the back foot to protect their lead as Evian enjoyed an extended period on top after the break.
Veretout played a key role in doubling his side's lead 15 minutes from time as his inviting cross was met with an emphatic finish from Yacine Bammou at the back post.
Evian were unable to respond in the closing stages as Nantes stretched their unbeaten run to six games in comfortable fashion.